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arXiv · 2004.04654

On the growth rate of geodesic chords

Simon Allais
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Abstract

We show that every forward complete Finsler manifold of infinite fundamental group and not homotopy-equivalent to $S^1$ has infinitely many geometrically distinct geodesics joining any given pair of points $p$ and $q$. In the special case in which $β_1(M;\mathbb{Z})\geq 1$ and $M$ is closed, the number of geometrically distinct geodesics between two points grows at least logarithmically.

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Simon Allais. 2020-04-09. On the growth rate of geodesic chords. https://doi.org/10.1016/j.difgeo.2020.101668

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